Identify the expression of x for which the following equation holds for every positive integers n and k: (2+²) = (₂²₁) +(²+¹). k+] k x = n + 1 x = n + 2 ○ x = n None of these. Determine the coefficient of x¹6,2¹ in the Binomial Theorem expansion of (3x² - y³)¹5. ○ - (15) 38 (15) 38 (¹5) - (15) None of these.

Q: In the expansion of (2 + 4y?) a. How many terms are in the expansion after like terms have been…

A: We will find the answers of all parts using binomial expansion.

Q: Find the coefficient of a-2 in the binomial expansion of  (27a2 - (1/81a3))9

A: Let us consider the expansion x+yn The binomial expansion is obtained as x+yn=∑k=0nCknxn-kyn

Q: a. Coefficient of x1/y21 in the expansion of (3x-2y)38 b. Coefficient of x23y41 in the expansion of…

A: The expression, nr can be defined by the formula, nr=n!(n-r)! r! .

Q: 24 + * ? 8 What is the coefficient for the yl8 term in the expansion of (5x°y²

A: We use the Binomial Theorem to answer the given question.

Q: (c) Find the term independent of x in the expansion of, 15 2 +

A:

Q: 10 Which term of the expansion of (x²+4) ¹º contains x 20 Term number contains x 20

A: